Heat milk, cream, sugar, salt, and espresso in a medium-sized saucepan over medium heat.
Stir constantly, until the mixture just reaches the point of simmer. Remove from heat.
While milk is heating, lightly whisk egg yolks in a separate medium-sized bowl.
Pour half of the warm milk/cream into the bowl with the egg yolks, whisking while you do so.
Then pour the egg/milk mixture back into the pan with the rest of the milk.
Continue to cook over low heat, while stirring with a wooden spoon. Stir for about 3-5 minutes, until the mixture thickens enough to coat the back of the spoon. Remove the saucepan from heat.
Strain egg/milk mixture into a separate large bowl.
Cover bowl with plastic wrap, making sure plastic wrap is touching top of the liquid so skin does not form, and refrigerate for at least 4 hours.
Once mixture is chilled, freeze in an ice cream maker according to the manufacturer’s instructions, mixing in Birthday Cake Oreo Cookies and sprinkles when ice cream is almost done processing.
Place ice cream in airtight containers and put in freezer for at least 4 hours to continue to harden.